Use the remainder theorem to find the remainder when f(x) is divided by x-(1/3). Then use the factor theorem to determine whether x-(1/3) is a factor of f(x).

f(x)= 3x^4-x^3+15x-5

Then is x-(1/3) a factor of f(x)?

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The remainder theorem states that the remainder of the division of a polynomial by a linear polynomial is equal to

To find the remainder when f(x) is divided by x-(1/3) using remainder theorem,

substitute x = 1/3 in f(x).

So the remainder is 0.

The factor theorem states that a polynomial has a factor if and only if .

We showed that .

Hence, by factor theorem is a factor of f(x).

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